An effective technique is applied to the suppression of vibrations in flexible rotor-bearing systems with small gyroscopic effects. A balanced linear-quadratic-Gaussian (LQG) controller design procedure is implemented. The size of the controller is reduced in two stages by using (i) a balanced model reduction, and (ii) an LQG balanced reduction. The condition for a gyroscopic matrix is developed that allows one to ignore the rotor gyroscopic effects in the process of the controller design, although they are included in the rotor dynamics. The approach is illustrated on a typical rotor-bearing system represented by a 48 degree-of-freedom finite element model.

1.
Adams
M. L.
, and
Padovan
J.
,
1981
, “
Insights into Linearized Rotor Dynamics
,”
Journal of Sound and Vibration
, Vol.
76
(
1
), pp.
129
142
.
2.
Anderson, B. D. O., and Moore, J. B., 1990, Optimal Control, Prentice Hall, Englewood Cliffs, NJ.
3.
Balas
M. J.
,
1978
, “
Feedback Control of Flexible Structures
,”
IEEE Transactions on Automatic Control
, Vol.
AC-23
, pp.
673
679
.
4.
Bendat, J. S., and Piersol, A. G., 1993, Engineering Applications of Correlation and Spectral Analysis, Wiley, New York.
5.
Blelloch
P. A.
,
Mingori
D. L.
, and
Wei
J. D.
,
1987
, “
Perturbation Analysis of Internal Balancing for Lightly Damped Mechanical Systems With Gyroscopic and Circulatory Forces
,”
AIAA Journal of Guidance, Control, and Dynamics
, Vol.
10
, pp.
406
410
.
6.
Childs
D.
,
1975
, “
Two Jeffcott-Based Simulation Models for Flexible Rotating Equipment
,”
ASME Journal for Industry
, Vol.
97
, pp.
1000
1014
.
7.
Fan
G. W.
,
Nelson
H. D.
,
Crouch
P. E.
, and
Mignolet
M. P.
,
1993
, “
LQG-Based Least-Squares Output Feedback Control of Rotor Vibrations Using the Complex Mode and Balanced Realization Methods
,”
ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER
, Vol.
115
, pp.
314
323
.
8.
Gawronski
W.
, and
Juang
J. N.
,
1990
, “
Model Reduction in Limited Time and Frequency Intervals
,”
International Journal of Systems Science
, Vol.
21
, pp.
349
376
.
9.
Gawronski, W., 1994, “A Balanced LQG Compensator for Flexible Structures,” Automatica, Vol. 30.
10.
Gawronski, W., and Sawicki, J. T., 1996, “Response Errors of Non-proportionally Lightly Damped Structures,” accepted for publication in Journal of Sound and Vibration.
11.
Gawronski, W., 1996, Balanced Control of Flexible Structures, Lecture Notes in Control and Information Sciences 211, Springer-Verlag, London.
12.
Genta
G.
,
1985
, “
Consistent Matrices in Rotor Dynamics
,”
Meccanica
, Vol.
20
, pp.
235
248
.
13.
Glasgow
D. A.
, and
Nelson
H. D.
,
1980
, “
Stability Analysis of Rotor Bearing Systems Using Component Mode Synthesis
,”
ASME Journal of Mechanical Design
, Vol.
102
, pp.
352
359
.
14.
Gregory
C. Z.
,
1984
, “
Reduction of Large Flexible Spacecraft Models Using Internal Balancing Theory
,”
AIAA Journal of Guidance, Control, and Dynamics
, Vol.
7
, pp.
725
732
.
15.
Jonckheere
A.
, and
Silverman
L. M.
,
1983
, “
A New Set of Invariants for Linear Systems—Application to Reduced Order Controller Design
,”
IEEE Trans. Autom. Control
, Vol.
AC-28
, pp.
953
964
.
16.
Jonckheere
A.
,
1984
, “
Principal Component Analysis of Flexible Systems—Open Loop Case
,”
IEEE Trans. Autom. Control
, Vol.
27
, pp.
1095
1097
.
17.
Kane
K.
, and
Torby
B. J.
,
1991
, “
The Extended Modal Reduction Method Applied to Rotor Dynamic Problems
,”
ASME Journal of Vibration and Acoustics
, Vol.
113
, pp.
79
84
.
18.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley-Interscience, New York.
19.
Li
D. F.
, and
Gunter
E. J.
,
1982
, “
Component Mode Synthesis of Large Rotor Systems
,”
ASME JOURNAL OF ENGINEERING FOR POWER
, Vol.
104
, pp.
525
532
.
20.
Maciejowski, J. M., 1989, Multivariable Feedback Design, Addison-Wesley, Wokingham, England.
21.
Meirovitch
L.
,
1974
, “
A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems
,”
AIAA Journal
, Vol.
12
, pp.
1337
1342
.
22.
Moore
B. C.
,
1981
, “
Principal Component Analysis in Linear Systems, Controllability, Observability and Model Reduction
,”
IEEE Transactions on Automatic Control
, Vol.
26
, pp.
17
32
.
23.
Opdenacker
P.
, and
Jonckheere
E. A.
,
1985
, “
LQG Balancing and Reduced LQG Compensation of Symmetric Passive Systems
,”
Int. J. Control
, Vol.
41
, No.
1
, pp.
73
109
, 1985.
24.
Palazzolo
A. B.
,
Lin
R. R.
,
Kascak
A. F.
, and
Alexander
R. M.
,
1989
, “
Active Control of Transient Rotordynamic Vibration by Optimal Control Methods
,”
ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER
, Vol.
111
, pp.
264
270
.
25.
Rouch
K. E.
, and
Kao
J. S.
,
1980
, “
Dynamic Reduction in Rotor Dynamics by the Finite Element Method
,”
ASME Journal of Mechanical Design
, Vol.
102
, pp.
360
368
.
26.
Salm, J., and Schweitzer, G., 1984, “Modelling and Control of a Flexible Rotor With Magnetic Bearings,” Proc. Conference on Vibrations in Rotating Machinery, York, United Kingdom, C277.
27.
Skelton, R. E., 1988, Dynamic System Control: Linear System Analysis and Synthesis, Wiley, New York.
28.
Tasaltin, R., 1992, “Active Vibration Control Strategies for a Flexible-Rotor Bearing System,” PhD Thesis, University of Bath, United Kingdom.
29.
Williams
T.
,
1990
, “
Closed Form Grammians and Model Reduction for Flexible Space Structures
,”
IEEE Transactions on Automatic Control
, Vol.
35
, pp.
379
382
.
This content is only available via PDF.
You do not currently have access to this content.